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Lecture 3 Supplement

Lecture 3 Supplement. Prof. Hsien-Hsin Sean Lee School of Electrical and Computer Engineering Georgia Institute of Technology. Rotation Along an Arbitrary Axis. Transform the axis to cross origin (0,0,0) Transform the axis around X onto the XZ plane

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Lecture 3 Supplement

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  1. Lecture 3 Supplement Prof. Hsien-Hsin Sean Lee School of Electrical and Computer Engineering Georgia Institute of Technology

  2. Rotation Along an Arbitrary Axis • Transform the axis to cross origin (0,0,0) • Transform the axis around X onto the XZ plane • Transform the axis around Y onto the Z axis • Perform Rotation (angle=) • Inverse Transform of 3. • Inverse Transform of 2. • Inverse Transform of 1.

  3. y x z Step 1: Translate to (0, 0, 0) • For easier viewing, I use RHS. Rotating axis

  4. y x z Step 2: Rotate around X, project to XZ y (a, b, c) b  z x (into the screen) c • Let’s pick up a random point (a, b, c) on the axis to figure out cos

  5. Step 3: Transform around Y onto the Z axis y a x y (into the screen)  x  (a’, 0, c’) z z

  6. Step 4: Perform Rotation (angle=) on Z

  7. Combine all matrices with Step 5, 6, 7

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